GATE CY Structure PYQs & Answers

Attempt a question, record the concept and assumptions, then check the available answer. Rework mistakes after revising the relevant concepts. Topic tags can overlap; review the question context.

Questions 1–10 of 46. Imported answers require independent review unless marked reviewed.

Topic practice 46 questionsPage 1 of 5

For the wavefunction

, where

is a constant, the correct statement(s) is(are)

Your answerSelect all correct options. You can choose more than one.

It represents a stationary state

It is an odd function

It represents the wavefunction of a particle moving on a circular ring of radius

It is an eigen function of the momentum operator

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The correct statement(s) about spherical harmonics (

) is(are)

Your answerSelect all correct options. You can choose more than one.

All spherical harmonics are complex functions

They are eigen functions of

The spherical harmonics

and

are degenerate

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The correct option for the average value of kinetic energy and the average value of potential energy of a one-dimensional harmonic oscillator with frequency

in its ground state is

Your answerChoose one option.

and

, respectively

and

, respectively

and

, respectively

and

, respectively

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The positions of two atoms in spherical polar coordinates (r, θ, Φ) are (1, π/2, π/2) and (1, π/4, 3π/2), where the distance is in Å and the angles are in radian. The interatomic distance (in Å) is _____ (rounded off to two decimal places).

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The orbital angular momentum (L) of an electron is

. The minimum angle between L and its z-component (in degrees) is _____ (rounded off to one decimal place).

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Rigid rotor wavefunctions are given by

. The wavefunctions

and

are given below

For a non-polar diatomic molecule, the value of transition dipole moment integral for transition between

and

is equal to

Your answerChoose one option.

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Consider two non-interacting particles confined to a one-dimensional box with infinite potential barriers. Their wavefunctions are

and

and energies are

and

, respectively. The INCORRECT statement(s) about this system is/are

Your answerSelect all correct options. You can choose more than one.

The total energy is

The total wavefunction is

The total energy is

The total wavefunction is

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The correct option with regard to the following statements is

(a) Time-independent Schrödinger equation can be exactly solved for Be

(b) For a particle confined in a one-dimensional box of length

with infinite potential barriers, the trial variation function

is not an acceptable trial wavefunction for

(c) Wavefunctions for system of Fermions must be anti-symmetric with respect to exchange of any two Fermions in the system.

(d) Born-Oppenheimer approximation can be used to separate the vibrational and rotational motion of a molecule.

Your answerChoose one option.

(a) True (b) False (c) False (d) True

(a) True (b) True (c) False (d) False

(a) False (b) True (c) True (d) False

(a) False (b) True (c) True (d) True

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Wavefunctions and energies for a particle confined in a cube box are

and

, respectively. The functions

, and

are written as linear combinations of

. Among these functions, the eigenfunction(s) of the Hamiltonian operator for this particle is/are

Your answerSelect all correct options. You can choose more than one.

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If a particle’s state function is an eigenfunction of the operator

with eigenvalue

, then the possible eigenvalue(s) of the operator

for the same state function is/are

Your answerSelect all correct options. You can choose more than one.

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GATE CY Structure PYQs

How to practice Structure

Question 27

Question 28

Question 45

Question 61

Question 65

Question 19

Question 28

Question 45

Question 56

Question 57